It might be differences between manufacturers as far as battery life. I bought a wireless trackball and wireless keyboard by Logitech two years ago and the verbiage on the Newegg description and on the boxes when I got them was the batteries were supposed to last 18 months. So far, they are right on schedule and I’ve only changed the batteries once. The trackball has absolutely no lag, but does stop responding on occasion maybe four times total?) and just has to be switched off and on again. Both devices have their own power save so I’ve never turned them off as a rule.
That’s precisely what I was thinking today. The latency, while intolerable at times, is definitely intermittent, and it doesn’t seem to be associated with computer lag. The mouse also seems to click randomly occasionally when the latency gets really bad, especially while dragging and dropping files. And I’m currently living out of a hotel room, so if the neighbors are using wireless devices, that’s probably the problem.
It’s a brand new mouse (Microsoft Wireless Mobile 3500) so the original battery probably was fine. Replacing it only seemed to fix the problem, temporarily. 
I have heard that using a piece of white paper as a mousing surface can help battery life because of sensors in the thing that adjust the internal light’s brightness (read it here among other places).
I haven’t tested this - I know I’d lose a wireless mouse, and the cable makes the wired one easier to find in my laptop bag.
Nor any time prior to that.
Some Wii wands just quit when the battery is low. This kid gives me his defunct Wii batteries. My old Logitech wireless mouse will run for days, sometimes weeks on old Wii batteries.
24
I’ve always had a wireless Microsoft mobile mouse for my laptop. The newest ones have an on/off switch on the bottom (along with a spot to insert the ‘nano’ receiver for storage when not in use.
This, Logitech just makes good hardware. They advertise an extended battery life often times a year or more. In my experience between personal use and conversation with others if you turn the mouse off while not in use the battery life will often exceed the advertised claims.
Gaming wise corded USB mice are always preferable to cordless. However that shouldn’t matter much outside of FPS games. MMORPGs definitely don’t suffer and Minecraft feels more like a slower paced MMORPG than a shooter IMO.
The lag has to be either interference or battery strength in your case though. I sit about 8’ away from my TV and use a wireless mouse to run my tablet on there via HDMI and I’ve never had a problem.